Geometric Sequence with Normal Distribution ProblemThe running time (in seconds) of an algorithm on a...

beatricalwu

beatricalwu

Answered

2022-07-19

Geometric Sequence with Normal Distribution Problem
The running time (in seconds) of an algorithm on a data set is approximately normally distributed with mean 3 and variance 0.25.
a. What is the probability that the running time of a run selected at random will exceed 2.6 seconds?
Answer for (a): I've computed this and found it to be p = 0.7881..
b. What is the probability that the running time of exactly one of four randomly selected runs will exceed 2.6 seconds?
Answer for (b): Not sure, I know it's a geometric sequence and I believe the formula that I need to use to be p ( 1 p ) 3 , thus giving me 0.7881 ( 1 0.7881 ) 3 however this was marked incorrect. I'm trying to figure out why, can someone explain my error and how to arrive at the correct solution?

Answer & Explanation

nuramaaji2000fh

nuramaaji2000fh

Expert

2022-07-20Added 18 answers

Step 1
You have 4 choices for which run will exceed 2.6 seconds. So your answer should be 4 p ( 1 p ) 3 instead of p ( 1 p ) 3 .
Step 2
You basically calculated the probability that a pre-determined run will exceed 2.6 seconds, and the other 3 runs are less than 2.6 seconds.

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